Preheat the oven to 400 degrees F.,Coat a large saute pan with olive oil, add the pancetta, and bring to medium-high heat.,Cook the pancetta until it starts to brown and crisp on the edges, 6 to 8 minutes.,Add the onions and season with salt.,Continue cooking until the onions are soft and aromatic, about 5 minutes.,Add the chopped mushroom stems, rosemary and garlic, and cook for another 2 to 3 minutes, stirring frequently.,Remove from the heat and place in a mixing bowl to cool.,______,Pour in 1 whisked egg and combine.,Add another egg if the mixture is still dry.,Make a 1- to 2-inch tester patty out of the stuffing mixture.,In a small saute pan, heat a bit of oil and cook the patty until it's done.,When cool enough, taste your tester patty to make sure it's delicious, if it's not, re-season.,When your tester tastes fabulous, generously fill each mushroom cap with the stuffing mixture and arrange them on a rimmed baking sheet.,Pour 1/4 to 1/3 cup water into the pan to keep the mushrooms moist.,Bake until the filling is cooked through and brown and crispy on the top, 8 to 10 minutes.,Transfer to serving platters.